The preseason All-American had nine first-half points but came alive in the paint after halftime.
The Lady Volunteers took a 39-31 lead on Glory Johnson's free throw with 17:39 left, but Griner had a pair of layups in an 11-2 run for the Lady Bears. The second gave Baylor a 42-41 lead with 15 minutes left.
Another Griner layup with 8:32 to play gave Baylor its ultimate lead, and the Lady Bears (6-0) relied on smothering defense to limit Tennessee to just 29.3 percent shooting.
Odyssey Sims added 23 points and Jordan Madden had 11 points for the Lady Bears, who also beat then-No. 2 Notre Dame on Nov. 20. They've got a Dec. 18 meeting with current No. 2 Connecticut.
Baylor entered the game averaging 53.8 rebounds per contest, but Tennessee (2-2) outmanned the Lady Bears on the glass 55-42.
The loss was the Lady Vols' 21st on their home court since moving to Thompson-Boling Arena in 1987. It ended a 38-game home winning streak — their third longest — dating back to a Feb. 16, 2009, loss to Duke.
It also marked the Lady Bears' third consecutive win against the Lady Vols, a rare feat by any team.
The game featured seven lead changes and three ties.
Baylor led by as many as eight points in the first half thanks to 10 of 11 shooting from the free-throw line. Tennessee found its way to the charity stripe too while fighting for points in the lane, and a pair of free throws and a 3-point shot by Stricklen helped erase the Lady Bears' lead.
Another 3-pointer by Stricklen with 5:51 in the first half knotted the score at 22 points, and Tennessee controlled the game through the rest of the half by taking charge of the boards.
Baylor shot just 34.5 percent in the first half but hit 48.4 percent after the break as Griner fought her way to the basket more. With every made layup, Griner seemed to relax a little more.
The Lady Vols tried doubling up on Griner, which only opened up opportunities for Sims and Madden. Sims hit a 3-pointer with 7:30 to go, and Madden had a trey of her own with 6:21 to play that gave Baylor a 59-55 lead.
Tennessee pulled within four points off a pair of free throws by Johnson with 2:03 left but would get no closer. On Baylor's next possession, Griner took an in-bound pass with 2 seconds on the shot clock and cleanly sank a jumper from the free throw line at the buzzer for a 67-61 lead with 1:32 left.
The matchup was dubbed a "We Back Pat" game in support of Tennessee coach Pat Summitt, who announced in August she had been diagnosed with early onset dementia, Alzheimer's type.
Both teams wore purple shirts that said "We Back Pat" while warming up, and Tennessee presented $75,000 checks from the proceeds of T-shirt sales to Alzheimer's Tennessee and the UT Medical Center for Alzheimer's research, treatment and education programs.
Summitt and son Tyler Summitt also announced at halftime they had created the Pat Summitt Foundation to further raise money for Alzheimer's programs.